I hope to meet someone with the same interest to go to discos and clubs with.I am looking forward to finding someone who will be a good friend and dancing partner.

Why not

I am looking forward to find someone who will be a good friend and dancing partner. or

I look forward to finding someone who will be a good friend and dancing partner.

These two I proposed are different in their meanings for me.

Furthermore I have a doubt about is it correct to use the word find with its the present participle form like verb due to the fact that the form finding is also a noun.

finding ~ a piece of information that is discovered during an official examination of a problem, situation or object:The report's finding on the decrease in violent crime supports the police chief's claims.(from a dictionary)

Tukanja wrote:Furthermore I have a doubt about is it correct to use the word find with its the present participle form like verb due to the fact that the form finding is also a noun.

finding ~ a piece of information that is discovered during an official examination of a problem, situation or object:The report's finding on the decrease in violent crime supports the police chief's claims.(from a dictionary)

After a bit more learning about and analysing the matter I would like to add the next

Seems to me that if I use the phrasal verb (form) "looking forward to", I may use the preposition "to" with the ordinary nouns such as bread, water, beauty queen, love, child etc.But if I use nouns which were made from a verb (gerund)then I prefer to use the preposition "towards" instead of the preposition "to".

Regarding the topic's original sentence my choice is next

I am looking forward towards finding someone who will be my good friend and dancing partner. ("towards" instead of "to")